I will define a discrete order or causal set, and state the Discrete-Continuum Correspondence (DCC) that expresses when a Lorentzian geometry (M,g) approximates a causal set (C, \prec). I will state the Hauptvermutung of causal set theory---essentially the conjecture that the DCC holds water---evidence for which will be the subject of this and the remaining two talks in the series. I will sketch the proof of the Penrose-Kronheimer-Hawking-Malament theorem that two distinguishing Lorentzian geometries are conformally isometric if and only if they have the same causal structure. This theorem, together with Riemann's insight that a discrete manifold contains its own metrical information in the counting measure, are the main grounds for confidence in the Hauptvermutung. I will explain why the prediction of causal set theory that there are no closed causal curves in the continuum theory is more than just ``assumption in, assumption out".